Aircraft: CRJ900
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Critical

Our flight prior to this incident was normal in every way. Nothing out of the ordinary occurred until approximately 40-45 minutes after takeoff.While at cruise at FL380; I noticed that our right engine oil pressure had turned yellow. It was around 35 psi. Although I had not seen one earlier in the flight; my first instinct was to check for a R OIL LEVEL LOW status message. Sure enough; there was a message there and upon observing the oil quantity; we saw that it was at 15%. Referencing the QRH; I read that if it is indicating 15% (it won't show any lower); the handbook advises you to complete the flight. I texted our Dispatcher that we would require maintenance when we reached[destination].A few minutes later; a master warning message displayed on our EICAS screen. It was 'R ENG OIL PRESSURE.' The oil pressure had dropped into the red zone. We immediately referenced the QRH and within just a few seconds had set the right thrust level to idle. Reading further in the procedure; it instructs you to complete an in-flight engine shutdown. I took my time and read through the text very carefully:If any 2 of the following 3 indications are displayed:L or R ENG OIL PRESS warning message;Affected engine oil pressure is below limits;Affected engine oil temperature is increasing or decreasing abnormally.Single Engine Procedures/In-Flight Engine Shutdown ..............................................ACCOMPLISHWhile we obviously had the warning message; the oil pressure was vacillating between red and yellow (25 and 26) for a short period. I was also a bit wary to shut down the engine since our oil temperature was not showing high nor was it climbing. It was showing almost the same as the left engine (within a few degrees) and was well within the green range. I did NOT want to shut an engine down unless ABSOLUTELY necessary. After a few moments; however; the oil pressure stayed constantly in the red range; and appeared to only be dropping. At that point we decided to go ahead with the in-flight shutdown.All the while; we had advised ATC of the situation and told them that we would be diverting to [a nearby alternate]. Per their instructions; we began to descend.Referencing our QRH; we proceeded to complete the in-flight shutdown of the right engine and all associated instructions. We started the APU as well. We did not expect the engine was damaged but did not want to attempt any restart of the engine (since it was very unlikely that the engine would just magically find more oil). We also completed the single engine landing portion of the QRH and made a note of all changes from the norm that would be associated with that. These included a flaps 20 landing; a higher than normal Vref speed; and additional runway length required.We [advised] ATC and advised them of fuel and souls on board. I was able to speak with our flight attendants and advise them of the situation. I sent a message to Dispatch informing them of our diversion and our situation. As we continued to descend; the First Officer got the ATIS; and we briefed the approach as well as completed the 'In-Range' checklist. I got the landing data from our ACARS and factored in our additional runway distance required. We had plenty.Our approach and landing were completed without any further issues. We were met with the fire trucks when we landed; which must be standard practice for any emergency aircraft landing. After arriving at the gate; I spoke with the airport representative and the fire department/police marshals and gave them any additional information that they required. Afterwards; I spoke with Dispatch and Maintenance Control and advised them of all that had happened and answered all questions that they asked. As far as I know and remember; no clearances were deviated from and all SOP were adhered to.I would like to end the narrative by complimenting everyone involved in this situation. From the flight attendants to ATC to the airport fire department; each and every entity was calm; collected; and extremely helpful in getting this aircraft down safely! The First Officer did an absolutely exceptional job; as well; as the pilot flying! My sincere thanks to all involved. This aircraft had been held the night before this incident due to the right engine not starting. The maintenance personnel had apparently fixed this issue; by installing a new starter I believe; and signed off the maintenance log. We had no problems starting the engine. I; admittedly; have no idea how the intricacies of the starter work; nor do I know if oil flows through there; but I think that it is possible that the two incidents could be related. If they are; then obviously something needs to be looked at.Whatever the root cause of the engine losing oil quantity and pressure was needs to be found out and fixed. CRJ-900 Captain reported diverting to an alternate airport after shutting down the right engine because of low oil pressure.